The project focuses on the harmonic analysis of transformer during the switching transient period. Measuring fundamental and second harmonics of differential current, an algorithm based on the Discrete Fourier Transform and an amplitude estimator are used to simulate and list various harmonic components of current and flux. Generalized functions for describing the relationships between resultant flux and harmonic components are derived. This is important to find these relations for further use in detecting non-linearity and elimination of harmonic components.
Harmonics in Transformer
A Seminar Report
In partial fulfillment for the award of the degree
CT INSTITUTE OF ENGINEERING, MANAGEMENT AND
CT INSTITUTE OF ENGINEERING, MANAGEMENT AND
SHAHPUR – JALANDHAR
I hereby certify that the work which is being presented in the Seminar entitled
“HARMONICS IN TRANSFORMERS” by “NIKHIL SHARMA” in partial fulfillment of
requirements for the award of degree of B.Tech. (Electrical Engineering) submitted in the
Department of Electrical Engineering at CTIEMT, Jalandhar is an authentic record of my
own work carried out during a period from July 2015 to Aug 2015 under the supervision of
Er.Akshay Agnihotri. The matter presented in this Seminar has not been submitted by me in
any other University / Institute for the award of B.Tech Degree.
This is to certify that the above statement made by the candidate is correct to the
best of my/our knowledge.
The B.Tech Viva-voice Examination of NAME has been held on
__________ and is accepted.
Er.Akshay Agnihotri (Supervisor)
Signature of HOD
The project focuses on the harmonic analysis of transformer during the switching transient
period. Measuring fundamental and second harmonics of differential current, an algorithm
based on the Discrete Fourier Transform and an amplitude estimator are used to simulate and
list various harmonic components of current and flux. Generalized functions for describing
the relationships between resultant flux and harmonic components are derived. This is
important to find these relations for further use in detecting non-linearity and elimination of
I would like to express my sincere gratitude to my Supervisors Er.Akshay Agnihotri for their
advices, guidance, continuous encouragement and their generous dedication of precious time
throughout the work of this thesis.
Furthermore, I would like to thank all of my friends for their help and support. Finally I
dedicate the thesis to all the members of my family for their moral support and patience
during this research work.
TABLE OF CONTENTS
Contents Page No.
Candidate’s Declaration 2
Table of Contents 5
List of Figures 6
Chapter 1: INTRODUCTION 7
Chapter 2: LITERATURE REVIEW 8-30
2.1 Harmonics 8
2.2 Single Phase Transformer 9
2.3 Three Phase Banks Of Single Phase Transformer 10
2.4 Three Phase Transformer Unit 11
2.5 Representation of Harmonics: the frequency Spectrum 12
2.6 Disturbances Caused By Non linear Loads 12
2.7 Flow of Harmonics in Distribution System 13
2.8 Why harmonics need to be detected and supressed 14
2.9 power and harmonics 16
2.10 Third harmonics in three phase transformer operation 17
2.11 Problems caused by harmonics current 21
2.12 Problems caused by harmonics voltage 24
2.13 Harmonics effect on transformer 27
Chapter 3: CONCLUSION RESEARCH AND FUTURE SCOPE 29-30
3.1 Conclusion 29
3.4 Suggestions for Future Scope 30
LIST OF FIGURES
Fig No. Figure Description Page
Fig 1.1 Harmonics generated by transformer 9
Fig 1.2 Frequency Spectrums 12
Fig 1.3 Single line diagram showing the impedance of supply 12
Fig 1.4 Diagram of installation supplying a non linear load 14
Fig 1.5 Diagram of same installation showing the phenomenon related to
h order harmonics 14
Fig 1.6 Flow of Harmonics current in a distribution system 14
Fig 1.7 Exicting current and neutral current in wye-wye transformer connection 18
Fig 1.8 Balanced Three phase waves containing a third harmonic components 19
Fig 1.9 Third harmonic voltage across an open corner in the delta 20
Harmonics are undesirable always whether it is current harmonics or voltage harmonics.
With increase dependency on non-linear loads it is necessary to use some arrangement which
can suppress, reduce, mitigate or eliminate the harmonics by which power quality and system
efficiency could improve. When non-linear loads are considerable part of the total load in the
facility (more than 20%) there is a chance of harmonic problem. There are two main affects
of harmonic currents on a distribution system. The first is that harmonic currents add to the
RMS value of the fundamental .This additional current will increase losses in bus bars, wire
and power factor correction capacitors used in the distribution system. The second affect is
the additional heating caused by each of the harmonic currents. The higher order harmonics
do not contribute to real work done. So these are always undesirable. Harmonics are the by
products of modern electronics. They occur frequently when there are a large number of
personal computers; uninterrupted power supplies (UPS), variable frequency drive (AC and
DC) or any electronic device using solid state power switching.
Large harmonics ,poor power factor and high THD in the utility interface are common
problems with non-linear loads such as adjustable speed drives induction heating systems ,
aircraft converter systems, industrial electronic equipment ,rectifier, microwave ovens
,blenders, TVs, which contains of power semiconductors connected to the electric
utility.These power semiconductors are some of the source of harmonics. Large
commercial and office buildings are supplied by a three phase utility source. The loads in
these buildings are usually fed primarily by single phase power lines connected between one
of the three lines and the neutral lines. Both non-linear and linear loads are connected to these
single phase distribution system.. Apart from unwanted losses in power systems,
harmonics may cause other undesirable effects like flickering of electronic displays, false
triggering of power electronic equipment and tripping of circuit breakers. Electronic energy
meters may record false reading, loading loss of revenue or related issues like relation
between service provider and service consumer. In the long run, harmonics reduces
life/efficiency of all electric/electronic equipment.
In addition to the operation of transformers on the sinusoidal supplies, the harmonic behavior
becomes important as the size and rating of the transformer increases. The effects of the
harmonic currents are
1. Additional copper losses due to harmonic currents
2. Increased core losses
3. Increased electromagnetic interference with communication circuits.
On the other hand the harmonic voltages of the transformer cause
1. Increased dielectric stress on insulation
2. Electro static interference with communication circuits.
3. Resonance between winding reactance and feeder capacitance.
In the present times a greater awareness is generated by the problems of harmonic voltages
and currents produced by non-linear loads like the power electronic converters. These
combine with non-linear nature of transformer core and produce severe distortions in voltages
and currents and increase the power loss. Thus the study of harmonics is of great practical
significance in the operation of transformers. The discussion here is confined to the
harmonics generated by transformers only.
Fig1.1 Harmonics Generated by Transformers
2.2 Single phase transformers
Modern transformers operate at increasing levels of saturation in order to reduce the weight
and cost of the core used in the same. Because of this and due to the hysteresis, the
transformer core behaves as a highly non-linear element and generates harmonic voltages and
currents. This is explained below. Fig. 34 shows the manner in which the shape of the
magnetizing current can be obtained and plotted. At any instant of the flux density wave the
ampere turns required to establish the same is read out and plotted, traversing the hysteresis
loop once per cycle. The sinusoidal flux density curve represents the sinusoidal applied
voltage to some other scale. The plot of the magnetizing current which is peaky is analyzed
using Fourier analysis. The harmonic current components are obtained from this analysis.
These harmonic currents produce harmonic fields in the core and harmonic voltages in the
windings. Relatively small value of harmonic fields generate considerable magnitude of
harmonic voltages. For example a 10% magnitude of 3rd harmonic flux produces 30%
magnitude of 3rd harmonic voltage. These effects get even more pronounced for higher order
harmonics. As these harmonic voltages get short circuited through the low impedance of the
supply they produce harmonic currents. These currents produce effects according to Lenz’s
law and tend to neutralize the harmonic flux and bring the flux wave to a sinusoid. Normally
third harmonic is the largest in its magnitude and hence the discussion is based on it. The
same can be told of other harmonics also. In the case of a single phase transformer the
harmonics are confined mostly to the primary side as the source impedance is much smaller
compared to the load impedance. The understanding of the phenomenon becomes more clear
if the transformer is supplied with a sinusoidal current source. In this case current has to be
sinusoidal and the harmonic currents cannot be supplied by the source and hence the induced
emf will be peaky containing harmonic voltages. When the load is connected on the
secondary side the harmonic currents flow through the load and voltage tends to become
sinusoidal. The harmonic voltages induce electric stress on dielectrics and increased electro
static interference. The harmonic currents produce losses and electromagnetic interference as
already noted above.
2.3 Three phase banks of single phase transformers
In the case of single phase transformers connected to form three phase bank, each
transformer is magnetically decoupled from the other. The flow of harmonic currents are
decided by the type of the electrical connection used on the primary and secondary sides.
Also, there are three fundamental voltages in the present case each displaced from the other
by 120 electrical degrees. Because of the symmetry of the a.c. wave about the time axis only
odd harmonics need to be considered. The harmonics which are triplen (multiples of three)
behave in a similar manner as they are co-phasal or in phase in the three phases. The non-
triplen harmonics behave in a similar manner to the fundamental and have ±120◦ phase
displacement between them. The harmonic behavior of poly-phase banks can be discussed
(i) Dd connection
In three phase banks with mesh connection on both primary side and secondary side a closed
path is available for the triplen harmonics to circulate currents. Thus the supply current is
nearly sinusoidal (but for the non-triplen harmonic currents). The triplen harmonic currents
inside the closed mesh winding correct the flux density wave to be nearly sinusoidal. The
secondary voltages will be nearly sinusoidal. Third harmonics currents flow both in the
primary and the secondary and hence the magnitudes of these currents, so also the drops due
to them will be lower.
(ii) Dy and Yd connection (without neutral connection)
Behavior of the bank with mesh connection on one side is similar to the one discussed under
Dd connection. The harmonic currents and drops and the departure of the flux density from
sinusoidal are larger in the present case compared to Dd banks.
(iii) Yy connection without neutral wires
With both primary and secondary connected in star no closed path exists. As the triplen
harmonics are always in phase, by virtue of the Y connection they get canceled in the line
voltages. Non-triplen harmonics like fundamental, become √ 3 times phase value and appear
in the line voltages. Line currents remain sinusoidal except for non-triplen harmonic currents.
Flux wave in each transformer will be flat topped and the phase voltages remain peaked. The
potential of the neutral is no longer steady. The star point oscillates due to the third harmonic
voltages. This is termed as ”oscillating neutral”.
(iv) Yy connection with neutral wires
When a neutral wire is provided the triplen harmonic current can flow and the condition is
similar to the single phase case (with a star connected 4 wire source or with the system earth).
The neutral wire carries three times the triplen harmonic current of one transformer as these
currents are co-phasal. Unloaded secondary neutral will not be operative. Other polyphase
connections not discussed above explicitly will fall under one type or the other of the cases
discussed. In a Yy connection, to obtain third harmonic suppression one may provide a third
winding which is connected in mesh, which can be an unloaded winding. It is called a
tertiary. This winding improves the single phase to earth fault detection also. Further, this
winding can be used to feed some permanent station loads also. Such transformers are
designated as Yyd transformers. If the neutral wires are provided and also mesh connected
winding is present, then triplen harmonics are ’shared’ between them depending upon their
2.4 Three phase transformers units
As against a bank of three single phase transformers connected to three phase mains, a three
phase transformer generally has the three magnetic circuits that are interacting. The exception
to this rule is a 3-phase shell type transformer. In the shell type of construction, even though
the three cores are together, they are non-interacting. Three limb core type 3-phase
transformer is the one in which the phases are magnetically also linked. Flux of each limb
uses the other two limbs for its return path. This is true for fundamental and non-triplen
harmonics. The triplen harmonics being co-phasal cannot use other limbs for the return path
(this holds good for zero sequence, unbalanced fundamental mmf also). The flux path is
completed through the air. So substantially large value of the mmf produces a low value of
third harmonic flux as the path of the flux is through the air and has a very high reluctance.
Thus the flux in the core remains nearly sinusoidal, so also the induced emf. This happens
irrespective of the type of connection used. The triplen order flux, sometimes links the tank
and produces loss in the same. Other harmonics can be suppressed by connecting tuned filters
at the terminals. Harmonic current compensation using special magnetic circuit design is
considered to be outside the scope here.
2.5 Representation of harmonics: the frequency spectrum
The frequency spectrum is a practical graphical means of representing the harmonics
contained in a periodic signal. The graph indicates the amplitude of each harmonic order.
This type of representation is also referred to as spectral analysis. The frequency spectrum
indicates which harmonics are present and their relative importance.
2.6 Disturbances causedby non-linear loads, i.e. current and voltage
The supply of power to non-linear loads causes the flow of harmonic currents in the
Voltage harmonics are caused by the flow of harmonic currents through the
impedances of the supply circuits
Note that the impedance of a conductor increases as a function of the frequency of
the current flowing through it. For each h-order harmonic current, there is therefore
an impedance Zh in the supply circuit.
The h-order harmonic current creates via impedance Zh a harmonic voltage Uh,
where Uh = Zh x Ih, i.e. a simple application of Ohm’s law. The voltage at B is therefore
distorted and all devices supplied downstream of point B will receive a distorted
Distortion increases in step with the level of the impedances in the distribution
system, for a given harmonic current.
2.7 Flow of harmonics in distribution systems
To better understand harmonic currents, it may be useful to imagine that the nonlinear
Loads reinject harmonic currents upstream into the distribution system, in the
direction of the source.
Figures 4a and 4b show an installation confronted with harmonic disturbances.
Figure 4a shows the flow of the fundamental 50 Hz current, whereas in 4b, the hth order
harmonic current is presented.
1.4 Diagram of an installationsupplying a non-linear load, showing only the fundamental 50 Hz current.
Fig1.5 Diagram of the same installation,showing only the phenomena related to the h-order harmonic.
Using once again the model of non-linear loads reinjecting harmonic currents into the
distribution system, it is possible to graphically represent this phenomena
Fig.1.6 Flow of harmonic currents in a distribution system.
2.8 Why harmonics need to be detected and suppressed ?
Disturbances caused by harmonics
In distribution systems, the flow of harmonics reduces power quality and
consequently causes a number of problems:
overloads on distribution systems due to the increase in the rms current
overloads on neutral conductors due to the summing of third-order harmonics
created by single-phase loads
overloads, vibrations and premature ageing of generators, transformers, motors,
etc., transformer hum
overloading and premature ageing of capacitors in power factor correction
distortion of the supply voltage, capable of disturbing sensitive loads
disturbances on communications networks and telephone lines.
The economic impact of disturbances
Harmonics have a significant economic impact, in that:
premature ageing of equipment means that it must be replaced earlier, unless it
was oversized to begin with
overloads on the distribution system mean the level of subscribed power must be
increased, with additional losses, unless the installation can be upgraded
distortion of the current provokes nuisance tripping and shutdown of production
These extra costs in terms of equipment, energy and productivity all contribute to
reducing the competitiveness of companies.
Increasingly serious consequences
As recently as ten years ago, harmonics were not considered a major problem,because their
effects on distribution systems were, generally speaking, relatively slight. However, the
massive increase in the use of loads employing power electronics has significantly worsened
the situation in all fields of activity.
Harmonics are all the more difficult to reduce in that they are often caused by
equipment that is vital to the operation of companies.
The essential indicators of harmonic distortion and measurement
2.9 Power and harmonics:-
(i) Active power:-
(ii) Distorsion power:-
2.10 Third Harmonics in 3-Phase Transformer Operation
It was shown that the sinusoidal flux in iron cores requires a third-harmonic component in the
exciting current, which, although small in relation to the rated current, may produce
undesirable effects in 3-phase transformer operation.
Consider three identical unloaded, single-phase transformers connected wye-wye to a 3-phase
generator with their primary neutral connected to the generator neutral as shown in Fig. 6-32.
The sum of the instantaneous currents flowing in the primary must equal zero, i.e.
The fundamental components, as well as harmonics - not including the third and multiples
thereof, are 120° apart, and, being of equal amplitudes, their sum is
where the subscript h stands for the order of the harmonics 1, 5, 7, 11, but not for 3, 9, 15,
etc. It should be remembered that harmonics in the exciting current of an iron-core
transformer are odd for sinusoidal flux when there is no d-c component of flux. It follows
from Eqs. 6-94 and 6-95 that the neutral current in the unloaded transformers, or in such as
deliver balanced sinusoidal 3-phase currents, is comprised of third-harmonic current, which is
the sum of the third harmonics in the three phases, thus
Figures show balanced 3-phase waves that are comprised of a fundamental and a third
harmonic. The sum of the three
Fig.1.7 Exciting currents and neutral current in wye-wye transformer connection.
Fig.1.8 Balanced 3-phase waves containing a fundamental and a third
harmonic component, (d) Sum of the three waves of (a), (b), and (c).
balanced waves is shown in Fig. 6-33(d) and is a pure third harmonic having an amplitude
equal to three times that of the third harmonic in any one phase.
If the neutral connection between the transformer primaries and the generator is broken, then
the path for the third-harmonic currents is interrupted and the third harmonics in the exciting
current will be suppressed. As a result, the flux cannot be sinusoidal, as it will contain a third
harmonic, which in turn produces a third harmonic in the transformer voltages. These third
harmonics show up only in the line-to-neutral voltage if the transformers are identical, and
will not appear in the line-to-line voltages because the line-to-line voltages are the phasor
difference between the line-to-neutral voltages, i.e.
The third harmonics in the line-to-neutral voltages of all three phases are equal and in phase
with each other and, therefore, cancel in the line-to-line
Fig.1.9 Third-harmonic voltage across an open corner in the delta on the secondary of a
wye-delta connection with the primary neutral isolated.
voltages. This becomes evident when the difference is taken between any two of three waves
a, b, and c of Fig. 6-33. Since
When the primaries are connected in delta, the third-harmonic components in the current are
free to flow, but will not show up in the line currents because the line currents are the
differences between the currents flowing in the delta as shown in Fig. 6-21. The delta
connection on the secondary side of a wye-delta arrangement also provides a path for the
third-harmonic components in the exciting mmf. Figure 6-34 shows the primaries of a wye-
delta arrangement connected in wye with the neutral isolated. One corner of the delta is
shown open. Since the neutral is isolated, there is no return path on the primary side for the
third harmonics in the exciting current, causing third harmonics to appear in the voltage
across each primary winding. There will be corresponding third harmonics in the voltages
across each secondary winding if one or more corners of the delta are open. The voltage
appearing across the open corner of the delta in Fig. 6-34 is the sum of the voltages in the
three secondary windings, and, if the exciting characteristics of the three phases are identical,
the sum of the fundamentals, as well as that of all harmonics - except the third and its
multiples - will be zero since these are all equal and 120° apart. The multiples of the third
harmonics are usually negligible. The third harmonics are equal and in phase with each other.
And the voltage across the open corner of the delta is three times the third-harmonic voltage
in one phase of the secondary. Thus, if V3 is the third harmonic voltage per phase in the delta,
then 3V3 is the voltage across the open corner of the delta.
Closing the open corner of the delta in Fig. 6-34, for normal operation, short circuits the
third-harmonic emf 3 V3, causing a third-harmonic current to circulate in the delta, thus
producing a substantially sinusoidal flux. If, in addition, the primary neutral is closed, the
third-harmonic components of the mmf required by the sinusoidal flux divide between the
primary and secondary, depending upon their relative third-harmonic leakage impedances.
Since the delta connection provides a path for the third-harmonic current, and because it
assures balanced voltages, most 3-phase transformations include a delta winding, which
makes the wye-delta or delta-wye arrangement very common. Where wye-wye
transformation is required, it is quite common to incorporate a third winding, known as a
tertiary, connected in delta. Generally, the rating of the delta-connected tertiary is
considerably lower than that of the primary and secondary wye-connected windings.
2.11 Problems causedby harmonic currents
(1) Neutral conductor over-heating
In a three-phase system the voltage waveform from each phase to the neutral so that,
when each phase is equally loaded, the°star point is displaced by 120 combined current in
the neutral is zero.
When the loads are not balanced only the net out of balance current flows in the neutral. In
the past, installers (with the approval of the standards authorities) have taken advantage of
this fact by installing half-sized neutral conductors. However, although the fundamental
currents cancel out, the harmonic currents do not – in fact those that are an odd multiple of
three times the fundamental, the ‘triple-N’ harmonics, add in the neutral.
The third°phase currents, are introduced at 120 harmonic of each phase is identical, being
three times the frequency and one-third of a (fundamental) cycle offset.
The effective third harmonic neutral current is shown at the bottom. In this case, 70% third
harmonic current in each phase results in 210% current in the neutral.
Case studies in commercial buildings generally show neutral currents between 150% and
210% of the phase currents, often in a half-sized conductor!
There is some confusion as to how designers should deal with this issue.
The simple solution, where single-cored cables are used, is to install a double sized
neutral, either as two separate conductors or as one single large conductor.
The situation where multi-cored cables are used is not so simple. The ratings of multi-core
cables (for example as given in IEC 60364–5-523 Table 52 and BS 7671 Appendix 4)
assume that the load is balanced and the neutral conductor carries no current, in other
words, only three of the four or five cores carry current and generate heat. Since the cable
current carrying capacity is determined solely by the amount of heat that it can dissipate at
the maximum permitted temperature, it follows that cables carrying triple-N currents must
In the example illustrated above, the cable is carrying five units of current – three in the
phases and two in the neutral – while it was rated for three units. It should be de-rated to
about 60% of the normal rating.
IEC 60364-5-523 Annex C (Informative) suggests a range of de-rating factors according to
the triple-N harmonic current present. Figure 13 shows de-rating factor against triple-N
harmonic content for the de-rating described in IEC 60364-5-523 Annex C and for the
thermal method used above.
(2) Effects on transformers
Transformers are affected in two ways by harmonics.
Firstly, the eddy current losses, normally about 10% of the loss at full load, increase
with the square of the harmonic number.
In practice, for a fully loaded transformer supplying a load comprising IT equipment the
total transformer losses would be twice as high as for an equivalent linear load.
This results in a much higher operating temperature and a shorter life. In fact, under these
circumstances the lifetime would reduce from around 40 years to more like 40 days!
Fortunately, few transformers are fully loaded, but the effect must be taken into account
when selecting plant.
The second effect concerns the triple-N harmonics. When reflected back to a delta
winding they are all in phase, so the triple-N harmonic currents circulate in the winding.
The triple-N harmonics are effectively absorbed in the winding and do not propagate onto
the supply, so delta wound transformers are useful as isolating transformers. Note that all
other, non triple-N, harmonics pass through. The circulating current has to be taken into
account when rating the transformer.
(3) Nuisance tripping of circuit breakers
Residual current circuit breakers (RCCB) operate by summing the current in the phase and
neutral conductors and, if the result is not within the rated limit, disconnecting the power
from the load. Nuisance tripping can occur in the presence of harmonics for two reasons.
Firstly, the RCCB, being an electromechanical device, may not sum the higher frequency
components correctly and therefore trips erroneously.
Secondly, the kind of equipment that generates harmonics also generates switching noise
that must be filtered at the equipment power connection. The filters normally used for this
purpose have a capacitor from line and neutral to ground, and so leak a small current to
This current is limited by standards to less than 3.5mA, and is usually much lower, but
when equipment is connected to one circuit the leakage current can be sufficient to trip the
RCCB. The situation is easily overcome by providing more circuits, each supplying fewer
Nuisance tripping of miniature circuit breakers (MCB) is usually caused because the
current flowing in the circuit is higher than that expected from calculation or simple
measurement due to the presence of harmonic currents.
Most portable measuring instruments do not measure true RMS values and can
underestimate non-sinusoidal currents by 40%.
(4) Over-stressing of power factor correction capacitors
Power-factor correction capacitors are provided in order to draw a current with a leading
phase angle to offset lagging current drawn by an inductive load such as induction motors.
The effective equivalent circuit for a PFC capacitor with a non-linear load. The impedance
of the PFC capacitor reduces as frequency rises, while the source impedance is generally
inductive and increases with frequency. The capacitor is therefore likely to carry quite
high harmonic currents and, unless it has been specifically designed to handle them,
damage can result.
A potentially more serious problem is that the capacitor and the stray inductance of the
supply system can resonate at or near one of the harmonic frequencies (which, of course,
occur at 100 Hz intervals). When this happens very large voltages and currents can be
generated, often leading to the catastrophic failure of the capacitor system.
Resonance can be avoided by adding an inductance in series with the capacitor such that
the combination is just inductive at the lowest significant harmonic. This solution also
limits the harmonic current that can flow in the capacitor. The physical size of the inductor
can be a problem, especially when low order harmonics are present.
(5) Skin effect
Alternating current tends to flow on the outer surface of a conductor. This is known as skin
effect and is more pronounced at high frequencies.
Skin effect is normally ignored because it has very little effect at power supply frequencies
but above about 350 Hz, i.e. the seventh harmonic and above, skin effect will become
significant, causing additional loss and heating. Where harmonic currents are present,
designers should take skin effect into account and de-rate cables accordingly.
Multiple cable cores or laminated bus bars can be used to help overcome this problem.
Note also that the mounting systems of bus bars must be designed to avoid mechanical
resonance at harmonic frequencies.
2.12 Problems caused by harmonic voltages
(1) voltage distortion
Because the supply has source impedance, harmonic load currents give rise to harmonic
voltage distortion on the voltage waveform (this is the origin of ‘flat topping’).
There are two elements to the impedance: that of the internal cabling from the point of
common coupling (PCC), and that inherent in the supply at the PCC, e.g. the local supply
The distorted load current drawn by the non-linear load causes a distorted voltage drop in
the cable impedance. The resultant distorted voltage waveform is applied to all other loads
connected to the same circuit, causing harmonic currents to flow in them – even if they are
Solution: The solution is to separate circuits supplying harmonic generating loads from
those supplying loads which are sensitive to harmonics, as shown in Figure 16. Here
separate circuits feed the linear and non-linear loads from the point of common coupling,
so that the voltage distortion caused by the non-linear load does not affect the linear load.
When considering the magnitude of harmonic voltage distortion it should be remembered
that when the load is transferred to a UPS or standby generator during a power failure the
source impedance and the resulting voltage distortion will be much higher.
Where local transformers are installed, they should be selected to have sufficiently low
output impedance and to have sufficient capacity to withstand the additional heating, in
other words, by selecting an appropriately over sized transformer.
Note that it is not appropriate to select a transformer design in which the increase in
capacity is achieved simply by forced cooling – such a unit will run at higher internal
temperatures and have a reduced service life. Forced cooling should be reserved for
emergency use only and never relied upon for normal running.
(2) Induction Motors
Harmonic voltage distortion causes increased eddy current losses in motors in the same
way as in transformers. However, additional losses arise due to the generation of harmonic
fields in the stator, each of which is trying to rotate the motor at a different speed either
forwards or backwards. High frequency currents induced in the rotor further increase
Where harmonic voltage distortion is present motors should be de-rated to take account of
the additional losses.
(3) Zero-crossing noise
Many electronic controllers detect the point at which the supply voltage crosses zero volts
to determine when loads should be turned on. This is done because switching inductive
loads at zero voltage does not generate transients, so reducing electromagnetic interference
(EMI) and stress on the semiconductor switching devices.
When harmonics or transients are present on the supply the rate of change of voltage at the
crossing becomes faster and more difficult to identify, leading to erratic operation. There
may in fact be several zero-crossings per half cycle.
(4)Harmonic problems affecting the supply
When a harmonic current is drawn from the supply it gives rise to a harmonic voltage drop
proportional to the source impedance at the point of common coupling (PCC) and the
Since the supply network is generally inductive, the source impedance is higher at higher
frequencies. Of course, the voltage at the PCC is already distorted by the harmonic
currents drawn by other consumers and by the distortion inherent in transformers, and each
consumer makes an additional contribution.
Remedies to Reduce Harmonic Problems:
(1) Over sizing Neutral Conductors
In three phase circuits with shared neutrals, it is common to oversize the neutral conductor
up to 200% when the load served consists of non-linear loads. For example, most
manufacturers of system furniture provide a 10 AWG conductor with 35 amp terminations
for a neutral shared with the three 12 AWG phase conductors.
In feeders that have a large amount of non-linear load, the feeder neutral conductor and
panel board bus bar should also be oversized.
(2) Using Separate Neutral Conductors
On three phase branch circuits, another philosophy is to not combine neutrals, but to run
separate neutral conductors for each phase conductor. This increases the copper use by
33%. While this successfully eliminates the addition of the harmonic currents on the
branch circuit neutrals, the panel board neutral bus and feeder neutral conductor still must
Oversizing Transformers and Generators: The oversizing of equipment for increased
thermal capacity should also be used for transformers and generators which serve
harmonics-producing loads. The larger equipment contains more copper.
(3) Passive filters
Passive filters are used to provide a low impedance path for harmonic currents so that they
flow in the filter and not the supply.
The filter may be designed for a single harmonic or for a broad band depending on
Simple series band stop filters are sometimes proposed, either in the phase or in the
neutral. A series filter is intended to block harmonic currents rather than provide a
controlled path for them so there is a large harmonic voltage drop across it.
This harmonic voltage appears across the supply on the load side. Since the supply voltage
is heavily distorted it is no longer within the standards for which equipment was designed
and warranted. Some equipment is relatively insensitive to this distortion, but some is very
sensitive. Series filters can be useful in certain circumstances, but should be carefully
applied; they cannot be recommended as a general purpose solution.
(4) Isolation transformers
As mentioned previously, triple-N currents circulate in the delta windings of transformers.
Although this is a problem for transformer manufacturers and specifies – the extra load has
to be taken into account it is beneficial to systems designers because it isolates triple-N
harmonics from the supply.
The same effect can be obtained by using a ‘zigzag’ wound transformer. Zigzag
transformers are star configuration auto transformers with a particular phase relationship
between the windings that are connected in shunt with the supply.
(5) Active Filters
The solutions mentioned so far have been suited only to particular harmonics, the isolating
transformer being useful only for triple-N harmonics and passive filters only for their
designed harmonic frequency. In some installations the harmonic content is less
In many IT installations for example, the equipment mix and location is constantly
changing so that the harmonic culture is also constantly changing. A convenient solution is
the active filter or active conditioner.
The active filter is a shunt device. A current transformer measures the harmonic content of
the load current, and controls a current generator to produce an exact replica that is fed
back onto the supply on the next cycle. Since the harmonic current is sourced from the
active conditioner, only fundamental current is drawn from the supply. In practice,
harmonic current magnitudes are reduced by 90%, and, because the source impedance at
harmonic frequencies is reduced, voltage distortion is reduced.
(6) K-Rated Transformers
Special transformers have been developed to accommodate the additional heating caused
by these harmonic currents. These types of transformers are now commonly specified for
new computer rooms and computer lab facilities.
(7) Special Transformers
There are several special types of transformer connections which can cancel harmonics.
For example, the traditional delta-wye transformer connection will trap all the triplen
harmonics (third, ninth, fifteenth, twenty-first, etc.) in the delta.
Additional special winding connections can be used to cancel other harmonics on balanced
loads. These systems also use more copper. These special transformers are often specified
in computer rooms with well balanced harmonic producing loads such as multiple input
mainframes or matched DASD peripherals.
While many filters do not work particularly well at this frequency range, special electronic
tracking filters can work very well to eliminate harmonics.
These filters are presently relatively expensive but should be considered for thorough
(9) Special Metering
Standard clamp-on ammeters are only sensitive to 60 Hertz current, so they only tell part
of the story. New “true RMS” meters will sense current up to the kilohertz range. These
meters should be used to detect harmonic currents. The difference between a reading on an
old style clamp-on ammeter and a true RMS ammeter will give you. an indication of the
amount of harmonic current present.
The measures described above only solve the symptoms of the problem. To solve the
problem we must specify low harmonic equipment. This is most easily done when
specifying electronic ballasts. Several manufacturers make electronic ballasts which
produce less than 15 % harmonics. These ballasts should be considered for any ballast
retrofit or any new project. Until low harmonics computers are available, segregating these
harmonic loads on different circuits, different panel boards or the use of transformers
should be considered. This segregation of “dirty” and “clean” loads is fundamental to
electrical design today. This equates to more branch circuits and more panel boards, thus
more copper usage.
2.13 Harmonics effect on Transformer
Harmonics distortion effect on Power System and their impact on Induction
Motors are already discussed.
Some of the disadvantages of harmonics and their impact on the transformers are:
RMS current increase
Eddy Current loss increases
DC offset current saturation
(i) RMS current Increase:
Harmonics currents in the system will increase the RMS current in the transformers. This
increase in the RMS current will increase the losses (copper losses) in the transformer which
results in the reduction of the overall efficiency of the transformer
(ii) Eddy Current Loss Increase:
Eddy currents loss is proportional to the square of the applied frequency. As the harmonic
components will have the frequencies of the order of multiples of the fundamental frequency
eddy current losses will increase with the presence of the harmonic components in the current
and voltage waveforms. Therefore because of the increase in the eddy current loss overall
efficiency of the transformer comes down. Harmonic component also increase the
temperature of the windings.
(iii) DC offset current saturation:
Due to the presence of dc component in the harmonics tend to saturate the core of the
A thorough understanding of electrical system-related problems will help us implement
better solutions. It is estimated that 70% of electrical loads are now non-linear. The
deterioration of the power factor will often be caused by harmonic currents (distortion factor)
and not by inductive loads (displacement factor).
To find a proper technique for correcting the power factor and reduce harmonic currents in
our system, the following must be considered:
• Determine the components of the total power factor.
• Correct the displacement factor at the inductive source (by adding capacitors).
• Correct the distortion factor at the harmonic source by reducing harmonic currents and
phase shifting systems.
3.2 Future Scope
The nonlinear magnetizing characteristics of most models did not account for core losses
(hysteresis loss and eddy current loss) precisely since it uses a constant resistor to represent
the loss. This is acceptable in some situations where the transformer serves not as a key
element of the simulated system such as in a transformer-converter motor system, but not in
others where it plays the major role such as in the inrush current calculations. The values of
the model elements in the duality based models are estimated from special test data. It may be
desirable to calculate them from physical dimensions and material characteristics that can be
obtained from the manufacturer. Also, most models available are for core type transformers
and a limited number of three phase connections has been modeled. There is not yet a clear
guide on how to model a three phase transformer with arbitrary connection and core type. If
possible, future works should address these subjects.